(a) The credit ratings for secondary school teachers who apply for a loan from a certain bank arenormally distributed with a mean of 200 and a standard deviation of 30.(i) Out of all such applicants over the next 6 months, what is the probability that a randomlyselected applicant will have a rating that is between 175 and 275? (ii) If a random sample of 40 such teachers are selected, giving a mean credit score of 180, whatproportion of applicants will have a rating that is more than 165? (b) The heights of students (X), doing a physical training course, can be modelled using a normalrandom variable with a mean of 160.5 cm and a variance of 9 cm. Determine the height of astudent, such that, this height is at least 60% of those that are doing the course.
(a) The credit ratings for secondary school teachers who apply for a loan from a certain bank are
normally distributed with a
(i) Out of all such applicants over the next 6 months, what is the probability that a randomly
selected applicant will have a rating that is between 175 and 275?
(ii) If a random sample of 40 such teachers are selected, giving a mean credit score of 180, what
proportion of applicants will have a rating that is more than 165?
(b) The heights of students (X), doing a physical training course, can be modelled using a normal
random variable with a mean of 160.5 cm and a variance of 9 cm. Determine the height of a
student, such that, this height is at least 60% of those that are doing the course.
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